Question

Question 1

1. Suppose you estimate the following regression function where Y, X1, and X2 are continuous variables measured in integers:

   Yhat=0.5+0.25*X1 −0.01*X2−0.43*X
3

   Suppose that X2=X1*X1

   The standard error of beta0hat is 0.10.

   The standard error of beta1hat is 0.05.

   The standard error of beta2hat is 0.005.

   The standard error of beta3hat is 0.05.

   What is the marginal effect of X1 when it increases from 3 to 4? Round to two decimal places.

10 points

Question 2

1. Refer to question 1 for estimation results. What is the marginal effect of X3? Round to two decimal places.

10 points

Question 3

1. Refer to question 1 for estimation results. What is the effect on Yhat when X1 increases from 11 to 15? Round to two decimal places.

10 points

Question 4

1. Does the relationship between X1 and Y exhibit diminishing marginal returns? Why or why not?

   		Yes, because beta2hat is negative and statistically significant.
   		No, because beta1hat is positive and beta2hat is negative, but beta2hat isn’t statistically significant.
   		No, because beta2hat is negative, but is not statistically significant.
   		Yes, because beta1hat is positive and statistically significant.
   		No, because beta1hat is positive, but is not statistically significant.
   		None of the above.
   		Yes, because beta1hat is positive and beta2hat is negative, and both are statistically significant.
   		No, because beta1hat and beta2hat are not statistically significant.

10 points

Question 5

1. Does the relationship between X3 and Y exhibit diminishing marginal returns? Why or why not?

   		Yes, because beta3hat is positive and beta2hat is negative, and both are statistically significant.
   		No, because beta3 and beta2 are not statistically significant.
   		Yes, because beta3hat is positive and statistically significant.
   		No, because beta3hat is positive and beta2hat is negative, but beta2 isn’t statistically significant.
   		No, because beta2 is negative, but is not statistically significant.
   		Yes, because beta2hat is negative and statistically significant.
   		No, because beta3hat is positive, but beta3 is not statistically significant.
   		None of the above.

10 points

Question 6

1. What is the turning point for X1 in the model? Round to one decimal place

Answer 1

Ans 1) Yhat = 0.5 + 0.25*X1 - 0.01*X2 - 0.43X3

We know that X2 = X1*X1 = (X1)²

therefore, Yhat = 0.5 + 0.25*X1 - 0.01*X1² - 0.43*X3

For calculating the marginal effect of X1 we will partial differentiate yhat with respect to X1.

Yhat/X1 = 0.25 - 0.02X1

Marginal effect of X1 when it increases from 3 to 4 is:

Yhat/X1 at 4 - Yhat/X1 at 3 = 0.25 - 0.02*4 - (0.25 - 0.02*3) = (-)0.02